A1 Journal article (refereed)
Geodesic ray transform with matrix weights for piecewise constant functions (2020)

Ilmavirta, Joonas; Railo, Jesse (2020). Geodesic ray transform with matrix weights for piecewise constant functions. Annales Academiae Scientiarum Fennicae-Mathematica, 45 (2), 1095-1102. DOI: 10.5186/aasfm.2020.4558

JYU authors or editors

Ilmavirta, Joonas

Railo, Jesse

Publication details

All authors or editors: Ilmavirta, Joonas; Railo, Jesse

Journal or series: Annales Academiae Scientiarum Fennicae-Mathematica

ISSN: 1239-629X

eISSN: 1798-2383

Publication year: 2020

Volume: 45

Issue number: 2

Pages range: 1095-1102

Publisher: Suomalainen tiedeakatemia

Publication country: Finland

Publication language: English

DOI: http://doi.org/10.5186/aasfm.2020.4558

Open Access: Publication published in an open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71316

Abstract

We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.

Keywords: inverse problems

Free keywords: geodesic ray transform; matrix weight; integral geometry

Fields of science:

111 Mathematics (Natural sciences)